In many artificial intelligence problems, the aim is to develop systems that use previous experience to acquire new skills more effectively. To fulfill this objective, meta-learning has been proposed as a framework that enables an agent to quickly learn a new task by leveraging an optimized initializer that is trained using similar tasks [1]}, [2]}, [3]}. One way to formulate the meta-learning problem is to cast it as a bi-level optimization problem [4]}, [5]}, [6]}, involving two loops: (i) an inner loop optimization that represents adaptation to a given task, and (ii) an outer loop optimization with the objective to train a meta-model. In [5]}, the authors proposed the model-agnostic meta-learning (MAML) formulation, which is shown to perform well in terms of convergence and fast adaptation to new task. However, despite its convergence and fast adaptation properties, solving MAML formulation requires backpropagation through the inner optimization process. Consequently, it requires higher-order derivative (Hessian's computation) which imposes high computational cost and vanishing gradients. These issues limit the scalability of MAML especially when the local models are multiple SGD steps from the initializer. First-order MAML (FOMAML) [5]} and Reptile [9]} are two first-order MAML-type algorithms which avoid second-order derivatives. Though both algorithms reduce the computational cost, they both ignore the dependence of task-models on the meta-models.
